A piggy bank has a total of 46 coins in it; some are dimes and some are quarters. If you have a total of $7.00, how many quarters and how many dimes do you have?

Question

whpalmer4 · Answer

You can write this as two equations with two variables. D will be the number of dimes, and Q will be the number of quarters. First equation will represent the number of coins of each type: D + Q = number of coins in the piggy bank Second equation will represent the value of the coins: *D +*Q = total value of money For the value, I would convert the dollars into cents because it is easier to avoid working with decimals for the coin values. You can do it either way, just be consistent. Finally, solve those two equations.

anonymous · Answer

Thanks beforehand, and so the equations would be,

D + Q = 46
&
.10D + .25Q = 7.00?

Now when you say solve, what exactly is it that I have to solve for? Combine both equations? Add one into the other to determine a value? Kinda confused on what exactly it is that I gotta' do, might seem a basic concept but it confuses me lol

mertsj · Answer

Why don't you rewrite the second equation so that is says 10D+25Q=700 and then replace D with 46-Q from the first equation and solve?

whpalmer4 · Answer

When you do the substitution of 46-Q in place of D in the second equation, you'll have an equation that only has Q as a variable.  You solve that for the value of Q.  When you have a value for Q, you put it back in D = 46-Q to find D.  

Last step is to put your values for D and Q in both equations and make sure that the result gives you 46 coins, and that the values add up to $7.00!  Especially with story or word problems, checking your answers is a good idea.

anonymous · Answer

Thanks guys I was able to solve it! :D

Q = 16, D = 30